Born in Takamatsu City, Kagawa Prefecture, Inokuma studied at the Tokyo School of Fine Arts from 1922-26 under the Western-style painter Fujishima Takeji (1865-1943). In 1935 he helped establish the Shin-Seisaku Kyokai, an artists' cultural organization, and he taught painting at the Tokyo School of Fine Arts from 1936-40. From 1945-55 he directed his own art school in Japan, completed numerous mural commissions in Japan and won the Mainichi Cultural and Artistic Award. Having moved to the United States in 1955, he was represented by the Willard Gallery in New York where he had ten one-man exhibitions between 1956-72. In 1963-64 he was in Contemporary Japanese Painting and Sculpture, an exhibition sponsored by the American Federation of Arts, and in numerous additional group shows at that time including the Carnegie International exhibition and the Sao Paulo Biennial.

The work of Inokuma Genichiro is in many museum collections including the National Museum of Art in Tokyo, the San Francisco Museum of Art, the Baltimore Museum of Art, the Institute of Contemporary Art in Boston, the Honolulu Academy of Art and the Marugame Genichiro-Inokuma Museum of Contemporary Art in Marugame City, Kagawa Prefecture.